Fluorescence polarization imaging of Sisyphus cooling in an atomic beam

Sisyphus cooling plays an important role in many cold atom applications including the formation of Bose-Einstein condensates and collimation of atomic beams. Here we present a method for measuring the localization of atoms by monitoring the polarization of fluorescence, providing a quantitative two-dimensional image of the cooling process. We outline the concept and provide theoretical models for the optical pumping, cooling, and channeling mechanisms, and present experimental data revealing the development of strong fluorescence polarization in an atomic beam during transverse $\left(\mathrm{lin}\perp \mathrm{lin}\right)$ cooling.

Figure 1

The interference of two orthogonally polarised, counterpropagating lasers leads to a position-dependent polarization seen by atoms and therefore differences in the internal energy levels of the ground states $m_F=\pm 1$, for an $F=1\to F=2$ transition. At an energy maxima an atom is more likely to absorb a photon and pass, via an excited state $\left|e\right.〉$, to the lower-energy ground state.

Figure 2

Fluorescence polarization imaging setup, with an atom beam collimated by two counterpropagating laser beams. The fluorescence $\mathbf{f}$ is measured in direction $x$, with polarization direction relative to the cooling laser beam axis $z$. The linear polarization is $I_{\parallel }$ $\left(I_{\perp }\right)$ when $\alpha =0^{\circ }$ $\left({90}^{\circ }\right)$ relative to the $z$ axis. In the experiment, hot ${}^{85}\mathrm{Rb}$ atoms are emitted from a recirculating candlestick source and initially collimated with two apertures. Sisyphus cooling is then applied and the cooling measured using the linear polarizer and fluorescence imaging camera (1), or a knife edge, a probe laser, and another camera (2).

Figure 3

${\mathrm{Rb}}^{85}$ energy level structure [21].

Figure 4

Evolution of the atomic ground state $F=3$ populations for a range of intensities $I$, for ${\sigma }^{+}$, linear (equal ${\sigma }^{+}$ and ${\sigma }^{-})$, and elliptical $\varphi =\pi /16,\pi /8$ polarizations. Detuning $\mathrm{\Delta }=0$ in all cases.

Figure 5

Steady-state populations for different light polarizations with $I=10I_{\mathrm{sat}}$, and corresponding line polarization $P_L$. $\delta z$ indicates the $z$ confinement range of the atoms inside a standing wave. The graph shows the calculated steady-state line polarization as a function of polarization angle $\varphi$ assuming $\delta z=0$.

Figure 6

Line polarizations for different intensities as a function of $y$ position through the cooling region for $L_{\min }=150$ mm $\left(\mathrm{\Delta }=-\mathrm{\Gamma }\right)$.

Figure 7

Knife-edge measurements of transverse polarization gradient cooling. Measurement geometry is shown at top, above CCD images and line profiles of the fluorescence intensity from intersection of the atom and probe laser beams, with (i) no transverse cooling, (ii) transverse cooling but no obstruction from the knife edge, and (iii) transverse cooling with knife edge. Bottom graph shows the spatial derivative of the knife-edge line profile.

Figure 8

False-color CCD images of fluorescence from the $\mathrm{lin}\perp \mathrm{lin}$ cooling region of the atom beam, with the polarizer at (i) $\alpha =0^{\circ }$, (ii) $\alpha ={90}^{\circ }$, and (iii) the resulting 2D line polarization. The plot shows a line profile through the center region of the polarization.

Figure 9

Knife-edge FWHM velocity spread measurements and minimum line polarization measurements as a function of light shift $U_o$ normalized to the recoil energy $E_r$, for a range of cooling laser detunings $\mathrm{\Delta }$.

Figure 10

Measured line polarization (blue) and quantum Monte Carlo simulation results (red).

Figure 11

Geometry of source and rectangular slit definining the initial beam prior to transverse cooling.